The four smallest cubic semisymmetric graphs are illustrated above. The smallest of these is Gray graph on 54 vertices, the next smallest
is the Iofinova-Ivanov graph on 110 vertices
(Iofinova and Ivanov 2002, Marušič et al. 2005), the third is
the Ljubljana graph (Conder et al. 2002),
and the fourth is the Tutte 12-cage.
Some cubic semisymmetric graphs are summarized in the following table.
Bouwer, I. A. "On Edge But Not Vertex Transitive Regular Graphs." J. Combin. Th. Ser. B12, 32-40, 1972.Conder,
M.; Malnič, A.; Marušič, D.; Pisanski, T.; and Potočnik, P.
"The Ljubljana Graph." 2002. http://citeseer.ist.psu.edu/conder02ljubljana.html.Ivanov,
A. V. "On Edge But Not Vertex Transitive Regular Graphs." In Combinatorial
Design Theory (Ed. C. J. Colbourn and R. Mathon). Amsterdam,
Netherlands: North-Holland, pp. 273-285, 1987.Iofinova, M. E.
and Ivanov, A. A. "Bi-Primitive Cubic Graphs." In Investigations
in the Algebraic Theory of Combinatorial Objects. pp. 123-134, 2002. (Vsesoyuz.
Nauchno-Issled. Inst. Sistem. Issled., Moscow, pp. 137-152, 1985.)Marušič,
D.; Pisanski, T.; and Wilson, S. "The Genus of the Gray Graph is 7." Europ.
J. Combin.26, 377-385, 2005.
